Question

A car is driven 210 km west and then 98 km southwest (45∘).

What is the displacement of the car from the point of origin (magnitude)?
What is the displacement of the car from the point of origin (direction)?

Answer 1

The displacement of the car from the point of origin is 308 km in magnitude and 45 degrees clockwise from the positive x-axis.

Step-by-step explanation:

To find the displacement of the car, we need to find the total distance and direction travelled. First, we calculate the total distance by adding the distances travelled in each direction: 210 km + 98 km = 308 km. Then, we can find the displacement by drawing a vector from the point of origin to the final position of the car, which is 308 km in magnitude. To find the direction of the displacement, we can use trigonometry. The angle between the west direction and the southwest direction is 45 degrees. Since southwest is located in the third quadrant of the coordinate system, the displacement direction is 45 degrees clockwise from the positive x-axis.

Answer 2

To find the displacement of the car, you can break down the motion into components and use vector addition. Then, use the Pythagorean theorem to find the magnitude and trigonometry to find the direction.

Step-by-step explanation:

To find the displacement of the car, we can break down the motion into x and y components and use vector addition. The car first travels 210 km west, which corresponds to a displacement of -210 km in the x-direction. Then, it travels 98 km southwest at an angle of 45 degrees. We can find the x and y components of this displacement by multiplying the distance by the cosine and sine of the angle, respectively. The x-component is -98 km * cos(45) and the y-component is -98 km * sin(45). To find the total displacement, we add the x-components and the y-components.

The magnitude of the displacement can be found using the Pythagorean theorem: displacement = √((x-displacement)² + (y-displacement)²). To find the direction of the displacement, we can use trigonometry. tan(theta) = y-displacement / x-displacement, so theta = atan(y-displacement / x-displacement).